Can maximum likelihood be used as a classifier?
If you read nothing else, maximum likelihood estimate => chance that the data predicted is the data observed. If you have a range of points (2, 3, 4, 5, 71) your MLE is going to favour ~4.5 because of means and standard deviations. MLE speeds up finding good input parameters, usually for a different classifier.

To answer your question: 

1) Columbia University have a great example of using MLE classifiers, where everything is broken down into bitesize (or bytesize) chunks. Read this. Seriously.

2) In short, MLE is best used for simple, univariable distributions. It doesn't scale well to big problems but is waaay faster than a Bayesian network for simple tasks like predicting your height based on the heights of your immediate relatives. If you want to get technical, the conditional probability network of the Bayesian model reveals insights faster than the chain multiplication of the more primitive MLE.

Hope it helps!